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Strings 2012 Munich July. (In)Stabilities and Complementarity in AdS/CFT. Eliezer Rabinovici The Hebrew University, Jerusalem Based on works with J.L.F Barbon Based on work with R. Auzzi, S. Elitzur and S.B. Gudnason.

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in stabilities and complementarity in ads cft

Strings 2012 Munich July

(In)Stabilities and Complementarity in AdS/CFT

Eliezer Rabinovici

The Hebrew University, Jerusalem

Based on works with J.L.F Barbon

Based on work with R. Auzzi, S. Elitzur and S.B. Gudnason


J. L. F. Barbon and E. Rabinovici, “AdS Crunches, CFT Falls And Cosmological Complementarity,”JHEP 1104, 044 (2011) [arXiv:1102.3015 [hep-th]].

  • J. L. F. Barbon and E. Rabinovici, “Holography of AdS vacuum bubbles,”JHEP 1004, 123 (2010) [arXiv:1003.4966 [hep-th]].
  • J. L .F. Barbon and E. Rabinovici, work in progress.
  • R. Auzzi, S. Elitzur, S. B. Gudnason and E. Rabinovici, “Time-dependent stabilization in AdS/CFT,”Accepted for publication in JHEP [arXiv:1206.2902 [hep-th]].
  • S. R. Coleman , F. De Luccia
  • T. Banks
  • T. Hertog , G. T. Horowitz, B. Craps, N. Turok, A. Bernamonti
  • S. Elitzur, A. Giveon, M. Porrati , E. Rabinovici
  • S. de Haro, I. Papadimitriou , A. C. Petkou
  • J. Orgera, J. Polchinski,; D. Harlow
  • J. Maldacena
  • Introduction
  • Bulk
  • AdS set up
  • Boundary
  • Complementarity
  • Butterflies
  • Geometry
  • Topology
  • Number of dimensions, small and large
  • (non-)Commutativity
  • Singularity structure
  • Associativity

Singularities express a breakdown of our knowledge/approximations

  • In general-covariantly invariant theories, singularities can hide behind horizons
  • Finite black hole entropy can be reconstructed from the outside
  • Can infinite entropy of a crunch be reconstructed as well?

In AdS what you see is not what you get

  • In AdS volume scales like
  • area for large enough
  • Area. The unstable
  • state can be stable or:


Non perturbative definition of the theory.

There are several possible QFT duals on the bondary


If the boundary theory is well defined so is the crunch in the bulk.

  • For the bulk crunch example above the boundary theory is well defined. Possible to describe a crunch.
  • It is well defined on a world volume which is dS but there is no gravitational coupling.
  • To see the crunch change coordinates on the boundary.

In the dS frame:

  • The World Volume expands(consider a slow expansion relative to other scales).
  • Time extends from -∞ to ∞
  • The couplings in the Lagrangian are time INDEPENDENT

In the E frame:

  • The world volume is static when it exists.
  • Time has a finite extension.
  • The relevant couplings in the Lagrangian are time dependent and explode at the end of time. The marginal operators remain time independent.

Over at the E-frame...

Mass term blows to

in finite time


A crunch can be described by a regular QFT on dS or by evolving with a state by a Hamiltonian which is well defined for a finite time range and then ceases to exist.

  • The two Hamiltonians do NOT commute.

One can build quantum mechanical models with two non-commuting Hamiltonians

t-evolution crunches and τ-evolution is eternal

but they are complementary as both time evolution

operators are related by a unitary canonical map


Bulk analogs

bubble of nothing

Continues to dS gap

and E-decoupling

Domain wall flow

Continues to dS condensate

and E-crunch


What about


This is the slightly massive UV CFT on a finite box

Detailed dynamics should depend on quantum effects

after large-N summation

In Bulk, we get linearized scalar flows which crunch

for either sign of

Small scalar flow

small large-N dS condensate

E-frame still crunches



An unstable marginal operator on the boundary is related to a Coleman de Luccia bubble in the bulk.


As seen on the boundary this crunch situation involves a flow to infinity at a finite time and need not be healed in the bulk.

Time dependent butterfly-like boundary potentialButterflies
  • Stable?
  • What is the dual theory in the bulk?

Positive effective potential

for drift mode

High frequencies

of oscillation


Free Field theory

Stability zones

Mathieu equation

Instability zones


For a < 2q instabilities are cured

  • For a > 2q resonances may appear
  • For compactified world volume resonances can be avoided (number theory results)
  • What about interacting boundary field theory?
    • It should thermalize
  • Go to the bulk
  • When the boundary theory is unstable, the bulk would crunch?
  • When the boundary theory is stabilized, then the bulk is healed?
  • An interacting boundary theory can thermalize and produce a black hole in the bulk?
  • Using AdS/CFT dictionary and numerical analysis



Crunch singularities

appearing in

a finite time

for low frequencies

black holes
Black holes

Black holes appearing

in a short time

black holes1
Black holes

Black holes appearing

only after

a long time

Waves bouncing

back and forth

  • Crunches can be described by complementary non commuting Hamiltonians. With or without drama.
  • Time dependent boundary Hamiltonians can heal crunch singularities.